On Geometric Optimization with Few Violated Constraints.
J. Matousek (1995)
Discrete & computational geometry
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Displaying similar documents to “Second-order necessary conditions for discrete inclusions with end point constraints”
On Geometric Optimization with Few Violated Constraints.
Unified duality for vector optimization problem over cones involving support functions
Surjeet Kaur Suneja, Pooja Louhan (2014)
RAIRO - Operations Research - Recherche Opérationnelle
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In this paper we give necessary and sufficient optimality conditions for a vector optimization problem over cones involving support functions in objective as well as constraints, using cone-convex and other related functions. We also associate a unified dual to the primal problem and establish weak, strong and converse duality results. A number of previously studied problems appear as special cases.
On constraint qualifications in directionally differentiable multiobjective optimization problems
Giorgio Giorgi, Bienvenido Jiménez, Vincente Novo (2010)
RAIRO - Operations Research
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We consider a multiobjective optimization problem with a feasible set defined by inequality and equality constraints such that all functions are, at least, Dini differentiable (in some cases, Hadamard differentiable and sometimes, quasiconvex). Several constraint qualifications are given in such a way that generalize both the qualifications introduced by Maeda and the classical ones, when the functions are differentiable. The relationships between them are analyzed. Finally, we give...
Sufficient Second Order Optimality Conditions for C^1 Multiobjective Optimization Problems
Gadhi, N. (2003)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: Primary 90C29; Secondary 90C30. In this work, we use the notion of Approximate Hessian introduced by Jeyakumar and Luc [19], and a special scalarization to establish sufficient optimality conditions for constrained multiobjective optimization problems. Throughout this paper, the data are assumed to be of class C^1, but not necessarily of class C^(1.1).
Tightly proper efficiency in vector optimization with nearly cone-subconvexlike set-valued maps.
Xu, Y.D., Li, S.J. (2011)
Journal of Inequalities and Applications [electronic only]
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Second-order optimality conditions for nondominated solutions of multiobjective programming with data
Liping Liu, Pekka Neittaanmäki, Michal Křížek (2000)
Applications of Mathematics
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We examine new second-order necessary conditions and sufficient conditions which characterize nondominated solutions of a generalized constrained multiobjective programming problem. The vector-valued criterion function as well as constraint functions are supposed to be from the class . Second-order optimality conditions for local Pareto solutions are derived as a special case.
On necessary optimality conditions in a class of optimization problems
Jiří V. Outrata (1989)
Aplikace matematiky
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In the paper necessary optimality conditions are derived for the minimization of a locally Lipschitz objective with respect to the consttraints , where is a closed set and is a set-valued map. No convexity requirements are imposed on . The conditions are applied to a generalized mathematical programming problem and to an abstract finite-dimensional optimal control problem.